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Explore the path integral formulation of pure 3D gravity on finite spacetime regions through this advanced theoretical physics seminar from the Institute for Advanced Study. Delve into boundary conditions that fix dihedral angles or geodesic lengths, and discover how these amplitudes calculate corrections to Gaussian statistics of operator product expansion (OPE) coefficients in dual conformal field theory. Learn about the connection between fixed-length path integrals and Virasoro topological quantum field theory, while examining the fixed-angle path integral as the partition function of Conformal Turaev-Viro theory—a novel topological theory based on triangulations. Understand how these two approaches relate through modular S-transforms and develop a comprehensive procedure for calculating exact path integrals on hyperbolic 3-manifolds by assembling generalized tetrahedra. Gain insights into concrete results for AdS3 spacetime and explore the potential applications of this statistical approach to gravitational path integrals in higher dimensions and de Sitter space, presented by Tom Hartman from Cornell University.
